A convenient setting for differential geometry and global analysis II
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Peter Michor (1984)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Kenderov, P. (1978)
Abstracta. 6th Winter School on Abstract Analysis
Luisa Fattorusso (2008)
Czechoslovak Mathematical Journal
Let be a bounded open subset of , . In we deduce the global differentiability result for the solutions of the Dirichlet problem with controlled growth and nonlinearity . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
Richard M. Aron, Paul D. Berner (1978)
Bulletin de la Société Mathématique de France
Esteban Andruchow (2003)
Studia Mathematica
Let ℳ be a type II₁ von Neumann algebra, τ a trace in ℳ, and L²(ℳ,τ) the GNS Hilbert space of τ. If L²(ℳ,τ)₊ is the completion of the set of selfadjoint elements, then each element ξ ∈ L²(ℳ,τ)₊ gives rise to a selfadjoint unbounded operator on L²(ℳ,τ). In this note we show that the exponential exp: L²(ℳ,τ)₊ → L²(ℳ,τ), , is continuous but not differentiable. The same holds for the Cayley transform . We also show that the unitary group with the strong operator topology is not an embedded submanifold...
Karlheinz Spallek (1972)
Manuscripta mathematica
James Glimm (1973/1974)
Séminaire Jean Leray
M. Breuer, Ch.D. Marshall (1978)
Mathematische Annalen
JESÚS A. JARAMILLO and ÁNGELES PRIETO M. ISABEL GARRIDO (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Aboubakr Bayoumi (2006)
Open Mathematics
We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex
J. Margalef-Roig, E. Outerelo-Domínguez, E. Padrón-Fernández (1997)
Rendiconti del Seminario Matematico della Università di Padova
Antonella Cabras, Ivan Kolář (1995)
Czechoslovak Mathematical Journal
Barnabas Garay (1990)
Studia Mathematica
George Graham (1984)
Czechoslovak Mathematical Journal
Paweł Urbański (1974)
J. Margalef-Roig, Enrique Outerelo-Domínguez (1994)
Archivum Mathematicum
In this paper we prove the existence of a closed neat embedding of a Hausdorff paracompact Hilbert manifold with smooth boundary into , where is a Hilbert space, such that the normal space in each point of a certain neighbourhood of the boundary is contained in . Then, we give a neccesary and sufficient condition that a Hausdorff paracompact topological space could admit a differentiable structure of class with smooth boundary.
Z. Ogrodzka (1973)
Colloquium Mathematicae
C. J. Atkin (2002)
Studia Mathematica
Let M be a separable Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a function, or of a section of a vector bundle, on the union of a closed submanifold and a closed locally compact set in M, extends to a function on the whole of M.
Seppo Hiltunen (1999)
Studia Mathematica
We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller -map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.
Cornelia Vizman (2011)
Archivum Mathematicum
Differential forms on the Fréchet manifold of smooth functions on a compact -dimensional manifold can be obtained in a natural way from pairs of differential forms on and by the hat pairing. Special cases are the transgression map (hat pairing with a constant function) and the bar map (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
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